The invention relates to a method and a device for determining a position of a mobile receiver RX which moves in an at least quasi-stationary environment. The determination of the position occurs here on the basis of signals s(t) which are emitted by a transmitter TX positioned immobile in the environment at time t=kT with time steps k and time increment T, wherein the receiver RX receives a signal s(kT) emitted by the transmitter TX, which is transmitted via N(k) transmission paths as signal components si(τ), as reception signal
            q      ⁡              (                  k          ,          τ                )              =                  ∑                  i          =          0                                      N            ⁡                          (              k              )                                -          1                    ⁢                        S          i                ⁡                  (          τ          )                      ,where k:=time step, τ:=time delay, and i=0, . . . , N(k)−1. In other words, a signal s(kT) emitted by the transmitter TX is thus transmitted via multipath propagation to the receiver RX. In multipath transmission, as interactions of the signal, the following are primarily taken into account: reflections of the signal components si(τ) at reflectors and/or scatterings of the signal components si(τ) at scatterers, on the different transmission paths.
Position determination, in addition to communication, is today one of the most important areas in which radio transmission of signals is used. The position determination here occurs by determining the propagation distance of a signal emitted by a transmitter TX with known position to a receiver RX. Under direct (quasi-optic) propagation conditions (“line of sight conditions”), the distance traveled by a signal emitted by a transmitter TX can be determined from the amplitude and the phase or time delay (“delay”) of the broadband signal received by the receiver. In order to determine a three-dimensional position of the receiver RX, the distances from at least three different transmitters TX must be determined, where it is assumed that the respective positions of the transmitters TXi are known, and the transmitters TXi and the receiver RX are time synchronized. Such positioning methods are used, for example, by base stations for mobile communication, global satellite navigation systems (GNSSs), special ultra-broadband transmitters, or WLAN base stations for “indoor” position detection.
Moreover, it is known that, in the case of a multipath reception of radio signals (“multipath reception”), the accuracy of the position determination is decreased if only a standard method for synchronizing, for example, the so-called “delay lock loop” method, is used for the position determination. Attempts to improve the accuracy of the position determination in multipath reception or the accuracy of the distance determination between transmitter TX and receiver RX are based in general on an estimate of the channel impulse response. Here, a quasi-optic, that is to say straight-line propagation of the partial signal from the transmitter to the receiver is assumed for the signal components si(τ) that arrive first. Examples of these methods can be obtained from the following publications:    F. Antreich, J. Nossek, and W. Utschick, “Maximum Likelihood Delay Estimation in a Navigation Receiver for Aeronautical Applications,” Aerospace Science and Technology, vol. 12, no. 3, Pages 256-267, 2008;    B. Krach, P. Robertson, and R. Weigel, “An Efficient Two-Fold Marginalized Bayesian Filter for Multipath Mitigation in GNSS Receivers,” EURASIP J. Adv. Sig. Proc., vol. 2010, 2010; and    P. Closas, C. Fernández-Predes, and J. A. Fernández-Rubio, “A Bayesian Approach to Multipath Mitigation in GNSS Receivers,” vol. 3, no. 4, Pages 695-706, August 2009.
These methods determine in each case the respective transmission distances of the individual signal components si(τ), or they determine the signal components si(τ) that arrive first at the receiver, so as to eliminate the influence of the other signal components si(τ) that arrive later. For the determination of a three-dimensional position of a receiver RX, these methods need at least three, and, if the receiver RX is not synchronized with the transmitters TXi, four different transmitters TXi, which in each case transmit signals to the receiver RX.
For uses in indoor position determination (“indoor positioning”) of a receiver RX, a method is known from the publication:    P. Meissner and K. Witrisal, “Multipath-Assisted Single-Anchor Indoor Localization in an Office Environment,” in IWSSIP, April 2012,which requires a transmitter with known position and known surrounding geometries (room layout) for the positioning of the receiver RX. In the process, reflected ultra-broadband signals are used for the positioning of the receiver RX, wherein both the room geometry, for example, the position and the orientation of the walls, and the position of the transmitter TX have to be known.